Question: Simplify the following expression: $p = \dfrac{-6z^2 + 90z - 300}{z - 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ p =\dfrac{-6(z^2 - 15z + 50)}{z - 5} $ Then we factor the remaining polynomial: $z^2 {-15}z + {50} $ ${-5} {-10} = {-15}$ ${-5} \times {-10} = {50}$ $ (z {-5}) (z {-10}) $ This gives us a factored expression: $\dfrac{-6(z {-5}) (z {-10})}{z - 5}$ We can divide the numerator and denominator by $(z + 5)$ on condition that $z \neq 5$ Therefore $p = -6(z - 10); z \neq 5$